… using differential equations#

This is treated in chapter 11.2 and 11.3 of the book Engineering Mechanics Volume 1 (Hartsuijker and Welleman, 2006).
Exercises#
Exercises in chapter 11.4 of the book Engineering Mechanics Volume 1 (Hartsuijker and Welleman, 2006), answers are available on this website: 11.1 - 11.11